Infinite dimensional SRB measures

Details Infinite dimensional SRB measures Infinite dimensional SRB measures

1995-10-02

arxiv.org/abs/chao-dyn/9509022v1

Nonlinear Sciences

Chaotic Dynamics

19 pages

Scientific paper

We review the basic steps leading to the construction of a Sinai-Ruelle-Bowen (SRB) measure for an infinite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of space-time correlations. First, using the Perron-Frobenius operator, one connects the dynamical system of coupled maps on a $d$-dimensional lattice to an equilibrium statistical mechanical model on a lattice of dimension $d+1$. This lattice model is, for weakly coupled maps, in a high-temperature phase, and we use a general, but very elementary, method to prove exponential decay of correlations at high temperatures.

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